pacman::p_load(sf, tidyverse, funModeling, blorr, corrplot, ggpubr, spdep, GWmodel, tmap, skimr, caret, berryFunctions)GWLR - Osun Water Points
case study : Modelling the Spatial Variation of the Explanatory Factors of Water Point Status using Geographically Weighted Logistic Regression (GWLR).
1. OVERVIEW
This study focuses on GWLR analysis based on Nigeria’s water points attributes.
1.1 Objectives
To build an explanatory model to discover factor affecting water point status in Osun State, Nigeria.
1.2 Study Area
Osun State, Nigeria
2. R PACKAGE REQUIRED
The following are the packages required for this exercise :
2.1 Load R Packages into R Environment
Usage of the code chunk below :
p_load( ) - pacman - to load packages. This function will attempt to install the package from CRAN or pacman repository list if its found not installed.
3. GEOSPATIAL DATA
3.1 Acquire Data Source
Aspatial Data
Osun_wp_sf.rds, contained water points within Osun state.
- It is in sf point data frame.
Geospatial Data
Osun.rds, contains LGAs boundaries of Osun State.
- It is in sf polygon data frame
3.2 Import Data
3.2.1 Import Boundary RDS File
bdy_osun <- read_rds("data/geodata/Osun.rds")3.2.1.1 review imported data
skim(bdy_osun)Warning: Couldn't find skimmers for class: sfc_MULTIPOLYGON, sfc; No user-
defined `sfl` provided. Falling back to `character`.| Name | bdy_osun |
| Number of rows | 30 |
| Number of columns | 5 |
| _______________________ | |
| Column type frequency: | |
| character | 5 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| ADM2_EN | 0 | 1 | 3 | 14 | 0 | 30 | 0 |
| ADM2_PCODE | 0 | 1 | 8 | 8 | 0 | 30 | 0 |
| ADM1_EN | 0 | 1 | 4 | 4 | 0 | 1 | 0 |
| ADM1_PCODE | 0 | 1 | 5 | 5 | 0 | 1 | 0 |
| geometry | 0 | 1 | 1805 | 7898 | 0 | 30 | 0 |
3.2.2 Import Attribute RDS
wp_osun <- read_rds("data/geodata/Osun_wp_sf.rds")3.2.2.1 review imported data
skim(wp_osun)Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.| Name | wp_osun |
| Number of rows | 4760 |
| Number of columns | 75 |
| _______________________ | |
| Column type frequency: | |
| character | 47 |
| logical | 5 |
| numeric | 23 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| source | 0 | 1.00 | 5 | 44 | 0 | 2 | 0 |
| report_date | 0 | 1.00 | 22 | 22 | 0 | 42 | 0 |
| status_id | 0 | 1.00 | 2 | 7 | 0 | 3 | 0 |
| water_source_clean | 0 | 1.00 | 8 | 22 | 0 | 3 | 0 |
| water_source_category | 0 | 1.00 | 4 | 6 | 0 | 2 | 0 |
| water_tech_clean | 24 | 0.99 | 9 | 23 | 0 | 3 | 0 |
| water_tech_category | 24 | 0.99 | 9 | 15 | 0 | 2 | 0 |
| facility_type | 0 | 1.00 | 8 | 8 | 0 | 1 | 0 |
| clean_country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| clean_adm1 | 0 | 1.00 | 3 | 5 | 0 | 5 | 0 |
| clean_adm2 | 0 | 1.00 | 3 | 14 | 0 | 35 | 0 |
| clean_adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| clean_adm4 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| installer | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management_clean | 1573 | 0.67 | 5 | 37 | 0 | 7 | 0 |
| status_clean | 0 | 1.00 | 9 | 32 | 0 | 7 | 0 |
| pay | 0 | 1.00 | 2 | 39 | 0 | 7 | 0 |
| fecal_coliform_presence | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| subjective_quality | 0 | 1.00 | 18 | 20 | 0 | 4 | 0 |
| activity_id | 4757 | 0.00 | 36 | 36 | 0 | 3 | 0 |
| scheme_id | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| wpdx_id | 0 | 1.00 | 12 | 12 | 0 | 4760 | 0 |
| notes | 0 | 1.00 | 2 | 96 | 0 | 3502 | 0 |
| orig_lnk | 4757 | 0.00 | 84 | 84 | 0 | 1 | 0 |
| photo_lnk | 41 | 0.99 | 84 | 84 | 0 | 4719 | 0 |
| country_id | 0 | 1.00 | 2 | 2 | 0 | 1 | 0 |
| data_lnk | 0 | 1.00 | 79 | 96 | 0 | 2 | 0 |
| water_point_history | 0 | 1.00 | 142 | 834 | 0 | 4750 | 0 |
| clean_country_id | 0 | 1.00 | 3 | 3 | 0 | 1 | 0 |
| country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| water_source | 0 | 1.00 | 8 | 30 | 0 | 4 | 0 |
| water_tech | 0 | 1.00 | 5 | 37 | 0 | 20 | 0 |
| adm2 | 0 | 1.00 | 3 | 14 | 0 | 33 | 0 |
| adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management | 1573 | 0.67 | 5 | 47 | 0 | 7 | 0 |
| adm1 | 0 | 1.00 | 4 | 5 | 0 | 4 | 0 |
| New Georeferenced Column | 0 | 1.00 | 16 | 35 | 0 | 4760 | 0 |
| lat_lon_deg | 0 | 1.00 | 13 | 32 | 0 | 4760 | 0 |
| public_data_source | 0 | 1.00 | 84 | 102 | 0 | 2 | 0 |
| converted | 0 | 1.00 | 53 | 53 | 0 | 1 | 0 |
| created_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| updated_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| Geometry | 0 | 1.00 | 33 | 37 | 0 | 4760 | 0 |
| ADM2_EN | 0 | 1.00 | 3 | 14 | 0 | 30 | 0 |
| ADM2_PCODE | 0 | 1.00 | 8 | 8 | 0 | 30 | 0 |
| ADM1_EN | 0 | 1.00 | 4 | 4 | 0 | 1 | 0 |
| ADM1_PCODE | 0 | 1.00 | 5 | 5 | 0 | 1 | 0 |
Variable type: logical
| skim_variable | n_missing | complete_rate | mean | count |
|---|---|---|---|---|
| rehab_year | 4760 | 0 | NaN | : |
| rehabilitator | 4760 | 0 | NaN | : |
| is_urban | 0 | 1 | 0.39 | FAL: 2884, TRU: 1876 |
| latest_record | 0 | 1 | 1.00 | TRU: 4760 |
| status | 0 | 1 | 0.56 | TRU: 2642, FAL: 2118 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| row_id | 0 | 1.00 | 68550.48 | 10216.94 | 49601.00 | 66874.75 | 68244.50 | 69562.25 | 471319.00 | ▇▁▁▁▁ |
| lat_deg | 0 | 1.00 | 7.68 | 0.22 | 7.06 | 7.51 | 7.71 | 7.88 | 8.06 | ▁▂▇▇▇ |
| lon_deg | 0 | 1.00 | 4.54 | 0.21 | 4.08 | 4.36 | 4.56 | 4.71 | 5.06 | ▃▆▇▇▂ |
| install_year | 1144 | 0.76 | 2008.63 | 6.04 | 1917.00 | 2006.00 | 2010.00 | 2013.00 | 2015.00 | ▁▁▁▁▇ |
| fecal_coliform_value | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| distance_to_primary_road | 0 | 1.00 | 5021.53 | 5648.34 | 0.01 | 719.36 | 2972.78 | 7314.73 | 26909.86 | ▇▂▁▁▁ |
| distance_to_secondary_road | 0 | 1.00 | 3750.47 | 3938.63 | 0.15 | 460.90 | 2554.25 | 5791.94 | 19559.48 | ▇▃▁▁▁ |
| distance_to_tertiary_road | 0 | 1.00 | 1259.28 | 1680.04 | 0.02 | 121.25 | 521.77 | 1834.42 | 10966.27 | ▇▂▁▁▁ |
| distance_to_city | 0 | 1.00 | 16663.99 | 10960.82 | 53.05 | 7930.75 | 15030.41 | 24255.75 | 47934.34 | ▇▇▆▃▁ |
| distance_to_town | 0 | 1.00 | 16726.59 | 12452.65 | 30.00 | 6876.92 | 12204.53 | 27739.46 | 44020.64 | ▇▅▃▃▂ |
| rehab_priority | 2654 | 0.44 | 489.33 | 1658.81 | 0.00 | 7.00 | 91.50 | 376.25 | 29697.00 | ▇▁▁▁▁ |
| water_point_population | 4 | 1.00 | 513.58 | 1458.92 | 0.00 | 14.00 | 119.00 | 433.25 | 29697.00 | ▇▁▁▁▁ |
| local_population_1km | 4 | 1.00 | 2727.16 | 4189.46 | 0.00 | 176.00 | 1032.00 | 3717.00 | 36118.00 | ▇▁▁▁▁ |
| crucialness_score | 798 | 0.83 | 0.26 | 0.28 | 0.00 | 0.07 | 0.15 | 0.35 | 1.00 | ▇▃▁▁▁ |
| pressure_score | 798 | 0.83 | 1.46 | 4.16 | 0.00 | 0.12 | 0.41 | 1.24 | 93.69 | ▇▁▁▁▁ |
| usage_capacity | 0 | 1.00 | 560.74 | 338.46 | 300.00 | 300.00 | 300.00 | 1000.00 | 1000.00 | ▇▁▁▁▅ |
| days_since_report | 0 | 1.00 | 2692.69 | 41.92 | 1483.00 | 2688.00 | 2693.00 | 2700.00 | 4645.00 | ▁▇▁▁▁ |
| staleness_score | 0 | 1.00 | 42.80 | 0.58 | 23.13 | 42.70 | 42.79 | 42.86 | 62.66 | ▁▁▇▁▁ |
| location_id | 0 | 1.00 | 235865.49 | 6657.60 | 23741.00 | 230638.75 | 236199.50 | 240061.25 | 267454.00 | ▁▁▁▁▇ |
| cluster_size | 0 | 1.00 | 1.05 | 0.25 | 1.00 | 1.00 | 1.00 | 1.00 | 4.00 | ▇▁▁▁▁ |
| lat_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| lon_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| count | 0 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▇▁▁ |
3.3 Exploratory Data Analysis (EDA)
3.3.1 Plot Bar Chart
3.3.1.1 visualise “status”
wp_osun %>%
freq(input = "status")Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
Please report the issue at <https://github.com/pablo14/funModeling/issues>.
status frequency percentage cumulative_perc
1 TRUE 2642 55.5 55.5
2 FALSE 2118 44.5 100.03.3.1.2 visualise “status” by “water_tech_category”
cross_plot(data = wp_osun, input = "water_tech_category", target = "status")
3.3.1.3 visualise “status” by “usage_capacity”
cross_plot(data = wp_osun, input = "usage_capacity", target = "status")
3.3.2 Visualise Distribution of “status” Variable
tmap_mode("view")tmap mode set to interactive viewingtm_shape(bdy_osun) +
tm_polygons(alpha = 0.4) +
tm_shape(wp_osun) +
tm_dots(col = "status",
alpha = 0.6) +
tm_view(set.zoom.limits = c(8.5,12))tmap_mode("plot")tmap mode set to plotting3.4 Data Wrangling
3.4.1 Edit Key Variables
wp_osun.sf <- wp_osun %>%
filter_at(vars(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean),
all_vars(!is.na(.)))%>%
mutate(usage_capacity = as.factor(usage_capacity))Remarks :
Convert “usage_capacity” from numeric to categorical variable via as.factor( ) function.
3.4.2 Get Column Index
match(c("distance_to_primary_road",
"distance_to_secondary_road",
"distance_to_tertiary_road",
"distance_to_city",
"distance_to_town",
"water_point_population",
"local_population_1km",
"usage_capacity",
"is_urban",
"water_source_clean",
"status",
"geometry"),
names(wp_osun.sf)) [1] 35 36 37 38 39 42 43 46 47 7 57 NA3.4.3 Create Correlation Analysis Data Table
wp_osun.sf_clean <- wp_osun.sf %>%
select(c(7, 35:39, 42:43, 46:47, 57)) %>%
st_set_geometry(NULL)4. CORRELATION ANALYSIS
4.1 Visualise Correlation Matrix
cluster_vars.cor = cor(wp_osun.sf_clean[,2:7])
corrplot.mixed(cluster_vars.cor,
lower = "ellipse",
upper = "number",
tl.pos = "lt",
diag = "l",
tl.col = "black")
Remarks :
The correlation matrix above indicated there is no highly correlated variable pairs.
5. LOGISTIC REGRESSION MODEL
5.1 Build Logistic Regression Model
model <- glm(status ~
distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
data = wp_osun.sf,
family = binomial(link = 'logit'))5.1.1 Create Model Overview :: model
blr_regress(model) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4744 TRUE
------------------------------------------------------------------------
Response Summary
--------------------------------------------------------
Outcome Frequency Outcome Frequency
--------------------------------------------------------
0 2114 1 2642
--------------------------------------------------------
Maximum Likelihood Estimates
-----------------------------------------------------------------------------------------------
Parameter DF Estimate Std. Error z value Pr(>|z|)
-----------------------------------------------------------------------------------------------
(Intercept) 1 0.3887 0.1124 3.4588 5e-04
distance_to_primary_road 1 0.0000 0.0000 -0.7153 0.4744
distance_to_secondary_road 1 0.0000 0.0000 -0.5530 0.5802
distance_to_tertiary_road 1 1e-04 0.0000 4.6708 0.0000
distance_to_city 1 0.0000 0.0000 -4.7574 0.0000
distance_to_town 1 0.0000 0.0000 -4.9170 0.0000
is_urbanTRUE 1 -0.2971 0.0819 -3.6294 3e-04
usage_capacity1000 1 -0.6230 0.0697 -8.9366 0.0000
water_source_cleanProtected Shallow Well 1 0.5040 0.0857 5.8783 0.0000
water_source_cleanProtected Spring 1 1.2882 0.4388 2.9359 0.0033
water_point_population 1 -5e-04 0.0000 -11.3686 0.0000
local_population_1km 1 3e-04 0.0000 19.2953 0.0000
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7347 Somers' D 0.4693
% Discordant 0.2653 Gamma 0.4693
% Tied 0.0000 Tau-a 0.2318
Pairs 5585188 c 0.7347
---------------------------------------------------------------5.1.2 Generate Confusion Matrix :: model
blr_confusion_matrix(model, cutoff = 0.5)Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
0 1301 738
1 813 1904
Accuracy : 0.6739
No Information Rate : 0.4445
Kappa : 0.3373
McNemars's Test P-Value : 0.0602
Sensitivity : 0.7207
Specificity : 0.6154
Pos Pred Value : 0.7008
Neg Pred Value : 0.6381
Prevalence : 0.5555
Detection Rate : 0.4003
Detection Prevalence : 0.5713
Balanced Accuracy : 0.6680
Precision : 0.7008
Recall : 0.7207
'Positive' Class : 1Remarks :
For a logistic regression model, the specificity rate is only 0.6154.
6. GEOGRAPHICALLY WEIGHTED LOGISTIC REGRESSION (GWLR) MODEL
6.1 Convert Simple Feature to SpatialPointsDataFrame
wp_osun.sp <- wp_osun.sf %>%
select(c(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
is_urban,
usage_capacity,
water_source_clean,
water_point_population,
local_population_1km)) %>%
as_Spatial()
wp_osun.spclass : SpatialPointsDataFrame
features : 4756
extent : 182502.4, 290751, 340054.1, 450905.3 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs
variables : 11
names : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, is_urban, usage_capacity, water_source_clean, water_point_population, local_population_1km
min values : 0, 0.014461356813335, 0.152195902540837, 0.017815121653488, 53.0461399623541, 30.0019777713073, 0, 1000, Borehole, 0, 0
max values : 1, 26909.8616132094, 19559.4793799085, 10966.2705628969, 47934.343603562, 44020.6393368124, 1, 300, Protected Spring, 29697, 36118 6.2 Fixed Bandwidth GWR Model
6.2.1 Compute Fixed Bandwidth
bw.fixed <- bw.ggwr(status ~ distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
data = wp_osun.sp,
family = "binomial",
approach = "AIC",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE)bw.fixedRemarks :
Recommended bandwidth is 2,599.672 metres.
6.2.2 Perform Fixed Bandwidth GWR Model
gwlr.fixed <- ggwr.basic(status ~
distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
data = wp_osun.sp,
bw = 2599.672,
family = "binomial",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE) Iteration Log-Likelihood
=========================
0 -1958
1 -1676
2 -1526
3 -1443
4 -1405
5 -1405 Remarks :
Calibrate the model with the recommended bandwidth, bw = 2,599.672.
gwlr.fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2022-12-18 00:34:53
Call:
ggwr.basic(formula = status ~ distance_to_primary_road + distance_to_secondary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town +
is_urban + usage_capacity + water_source_clean + water_point_population +
local_population_1km, data = wp_osun.sp, bw = 2599.672, family = "binomial",
kernel = "gaussian", adaptive = FALSE, longlat = FALSE)
Dependent (y) variable: status
Independent variables: distance_to_primary_road distance_to_secondary_road distance_to_tertiary_road distance_to_city distance_to_town is_urban usage_capacity water_source_clean water_point_population local_population_1km
Number of data points: 4756
Used family: binomial
***********************************************************************
* Results of Generalized linear Regression *
***********************************************************************
Call:
NULL
Deviance Residuals:
Min 1Q Median 3Q Max
-124.555 -1.755 1.072 1.742 34.333
Coefficients:
Estimate Std. Error z value Pr(>|z|)
Intercept 3.887e-01 1.124e-01 3.459 0.000543
distance_to_primary_road -4.642e-06 6.490e-06 -0.715 0.474422
distance_to_secondary_road -5.143e-06 9.299e-06 -0.553 0.580230
distance_to_tertiary_road 9.683e-05 2.073e-05 4.671 3.00e-06
distance_to_city -1.686e-05 3.544e-06 -4.757 1.96e-06
distance_to_town -1.480e-05 3.009e-06 -4.917 8.79e-07
is_urbanTRUE -2.971e-01 8.185e-02 -3.629 0.000284
usage_capacity1000 -6.230e-01 6.972e-02 -8.937 < 2e-16
water_source_cleanProtected Shallow Well 5.040e-01 8.574e-02 5.878 4.14e-09
water_source_cleanProtected Spring 1.288e+00 4.388e-01 2.936 0.003325
water_point_population -5.097e-04 4.484e-05 -11.369 < 2e-16
local_population_1km 3.451e-04 1.788e-05 19.295 < 2e-16
Intercept ***
distance_to_primary_road
distance_to_secondary_road
distance_to_tertiary_road ***
distance_to_city ***
distance_to_town ***
is_urbanTRUE ***
usage_capacity1000 ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring **
water_point_population ***
local_population_1km ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6534.5 on 4755 degrees of freedom
Residual deviance: 5688.0 on 4744 degrees of freedom
AIC: 5712
Number of Fisher Scoring iterations: 5
AICc: 5712.099
Pseudo R-square value: 0.1295351
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 2599.672
Regression points: the same locations as observations are used.
Distance metric: A distance matrix is specified for this model calibration.
************Summary of Generalized GWR coefficient estimates:**********
Min. 1st Qu. Median
Intercept -8.7229e+02 -4.9955e+00 1.7600e+00
distance_to_primary_road -1.9389e-02 -4.8031e-04 2.9618e-05
distance_to_secondary_road -1.5921e-02 -3.7551e-04 1.2317e-04
distance_to_tertiary_road -1.5618e-02 -4.2368e-04 7.6179e-05
distance_to_city -1.8416e-02 -5.6217e-04 -1.2726e-04
distance_to_town -2.2411e-02 -5.7283e-04 -1.5155e-04
is_urbanTRUE -1.9790e+02 -4.2908e+00 -1.6864e+00
usage_capacity1000 -2.0772e+01 -9.7231e-01 -4.1592e-01
water_source_cleanProtected.Shallow.Well -2.0789e+01 -4.5190e-01 5.3340e-01
water_source_cleanProtected.Spring -5.2235e+02 -5.5977e+00 2.5441e+00
water_point_population -5.2208e-02 -2.2767e-03 -9.8875e-04
local_population_1km -1.2698e-01 4.9952e-04 1.0638e-03
3rd Qu. Max.
Intercept 1.2763e+01 1073.2156
distance_to_primary_road 4.8443e-04 0.0142
distance_to_secondary_road 6.0692e-04 0.0258
distance_to_tertiary_road 6.6815e-04 0.0128
distance_to_city 2.3718e-04 0.0150
distance_to_town 1.9271e-04 0.0224
is_urbanTRUE 1.2841e+00 744.3099
usage_capacity1000 3.0322e-01 5.9281
water_source_cleanProtected.Shallow.Well 1.7849e+00 67.6343
water_source_cleanProtected.Spring 6.7663e+00 317.4133
water_point_population 5.0102e-04 0.1309
local_population_1km 1.8157e-03 0.0392
************************Diagnostic information*************************
Number of data points: 4756
GW Deviance: 2795.084
AIC : 4414.606
AICc : 4747.423
Pseudo R-square value: 0.5722559
***********************************************************************
Program stops at: 2022-12-18 00:35:49 gwr.fixed <- as.data.frame(gwlr.fixed$SDF)6.2.3 Set Threshold Value
Set this exercise’s threshold value, otherwise known as “yhat” to 0.5.
The value will be assigned to 1 when greater than 0.5, else 0, and saved under the “most” variable.
gwr.fixed <- gwr.fixed %>%
mutate(most = ifelse(
gwr.fixed$yhat >= 0.5, T, F
))6.2.3.1 visualise “most”
freq(gwr.fixed$most)Warning in freq(gwr.fixed$most): All input values are NA.NULL6.2.4 Generate Confusion Matrix
gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data = gwr.fixed$most, reference = gwr.fixed$y)
CMConfusion Matrix and Statistics
Reference
Prediction FALSE TRUE
FALSE 1824 263
TRUE 290 2379
Accuracy : 0.8837
95% CI : (0.8743, 0.8927)
No Information Rate : 0.5555
P-Value [Acc > NIR] : <2e-16
Kappa : 0.7642
Mcnemar's Test P-Value : 0.2689
Sensitivity : 0.8628
Specificity : 0.9005
Pos Pred Value : 0.8740
Neg Pred Value : 0.8913
Prevalence : 0.4445
Detection Rate : 0.3835
Detection Prevalence : 0.4388
Balanced Accuracy : 0.8816
'Positive' Class : FALSE
6.2.5 Visualise GWLR
6.2.5.1 extract administrative variables
wp_osun.sf_selected <- wp_osun.sf %>%
select(c(ADM2_EN, ADM2_PCODE, ADM1_EN, ADM1_PCODE, status))6.2.5.2 combine wp_osun.sf_selected and gwr.fixed
gwr_sf.fixed <- cbind(wp_osun.sf_selected, gwr.fixed)6.2.5.3 visualise coefficient estimates
tmap_mode("view")tmap mode set to interactive viewingprob_T <- tm_shape(bdy_osun) +
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed) +
tm_dots(col = "yhat",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(8.5,14))
prob_Ttmap_mode("plot")tmap mode set to plotting7 MODEL CALIBRATION
7.1 Calibrate Logistic Regression Model
Remove the insignificant variables “distance_to_primary_road” and “distance_to_secondary_road” that identified under section 5.2.
model_calibr <- glm(status ~ distance_to_tertiary_road+
distance_to_city+
distance_to_town+
water_point_population+
local_population_1km+
usage_capacity+
is_urban+
water_source_clean,
data = wp_osun.sf,
family = binomial(link = "logit"))7.2 Create Model Overview :: model_calibr
blr_regress(model_calibr) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4746 TRUE
------------------------------------------------------------------------
Response Summary
--------------------------------------------------------
Outcome Frequency Outcome Frequency
--------------------------------------------------------
0 2114 1 2642
--------------------------------------------------------
Maximum Likelihood Estimates
-----------------------------------------------------------------------------------------------
Parameter DF Estimate Std. Error z value Pr(>|z|)
-----------------------------------------------------------------------------------------------
(Intercept) 1 0.3540 0.1055 3.3541 8e-04
distance_to_tertiary_road 1 1e-04 0.0000 4.9096 0.0000
distance_to_city 1 0.0000 0.0000 -5.2022 0.0000
distance_to_town 1 0.0000 0.0000 -5.4660 0.0000
water_point_population 1 -5e-04 0.0000 -11.3902 0.0000
local_population_1km 1 3e-04 0.0000 19.4069 0.0000
usage_capacity1000 1 -0.6206 0.0697 -8.9081 0.0000
is_urbanTRUE 1 -0.2667 0.0747 -3.5690 4e-04
water_source_cleanProtected Shallow Well 1 0.4947 0.0850 5.8228 0.0000
water_source_cleanProtected Spring 1 1.2790 0.4384 2.9174 0.0035
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7349 Somers' D 0.4697
% Discordant 0.2651 Gamma 0.4697
% Tied 0.0000 Tau-a 0.2320
Pairs 5585188 c 0.7349
---------------------------------------------------------------7.3 Generate Confusion Matrix :: model_calibr
blr_confusion_matrix(model_calibr, cutoff = 0.5)Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
0 1300 743
1 814 1899
Accuracy : 0.6726
No Information Rate : 0.4445
Kappa : 0.3348
McNemars's Test P-Value : 0.0761
Sensitivity : 0.7188
Specificity : 0.6149
Pos Pred Value : 0.7000
Neg Pred Value : 0.6363
Prevalence : 0.5555
Detection Rate : 0.3993
Detection Prevalence : 0.5704
Balanced Accuracy : 0.6669
Precision : 0.7000
Recall : 0.7188
'Positive' Class : 1Remarks :
The specificity rate, 0.6149 is slightly lower than the original logistic regression model, which is 0.6154.
wp_osun.sp2 <- wp_osun.sf %>%
select(c(status,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean)) %>%
as_Spatial()
wp_osun.sp2class : SpatialPointsDataFrame
features : 4756
extent : 182502.4, 290751, 340054.1, 450905.3 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs
variables : 9
names : status, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean
min values : 0, 0.017815121653488, 53.0461399623541, 30.0019777713073, 0, 0, 1000, 0, Borehole
max values : 1, 10966.2705628969, 47934.343603562, 44020.6393368124, 29697, 36118, 300, 1, Protected Spring 7.4 Fixed Bandwidth GWR Model :: model_calibr
bw.fixed_calibr <- bw.ggwr(status ~ distance_to_tertiary_road+
distance_to_city+
distance_to_town+
water_point_population+
local_population_1km+
usage_capacity+
is_urban+
water_source_clean,
data = wp_osun.sp2,
family = 'binomial',
approach = 'AIC',
kernel = 'gaussian',
adaptive = FALSE,
longlat = FALSE)bw.fixed_calibrRemark :
The recommended bandwidth is 2,377.371 metres.
7.4.1 Compute Fixed Bandwidth
gwlr.fixed_calibr <- ggwr.basic(status ~ distance_to_tertiary_road +
distance_to_city +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = wp_osun.sp2,
bw = 2377.371,
family = 'binomial',
kernel = 'gaussian',
adaptive = FALSE,
longlat = FALSE) Iteration Log-Likelihood
=========================
0 -1959
1 -1680
2 -1531
3 -1447
4 -1413
5 -1413 gwlr.fixed_calibr ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2022-12-18 00:35:51
Call:
ggwr.basic(formula = status ~ distance_to_tertiary_road + distance_to_city +
distance_to_town + water_point_population + local_population_1km +
usage_capacity + is_urban + water_source_clean, data = wp_osun.sp2,
bw = 2377.371, family = "binomial", kernel = "gaussian",
adaptive = FALSE, longlat = FALSE)
Dependent (y) variable: status
Independent variables: distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km usage_capacity is_urban water_source_clean
Number of data points: 4756
Used family: binomial
***********************************************************************
* Results of Generalized linear Regression *
***********************************************************************
Call:
NULL
Deviance Residuals:
Min 1Q Median 3Q Max
-129.368 -1.750 1.074 1.742 34.126
Coefficients:
Estimate Std. Error z value Pr(>|z|)
Intercept 3.540e-01 1.055e-01 3.354 0.000796
distance_to_tertiary_road 1.001e-04 2.040e-05 4.910 9.13e-07
distance_to_city -1.764e-05 3.391e-06 -5.202 1.97e-07
distance_to_town -1.544e-05 2.825e-06 -5.466 4.60e-08
water_point_population -5.098e-04 4.476e-05 -11.390 < 2e-16
local_population_1km 3.452e-04 1.779e-05 19.407 < 2e-16
usage_capacity1000 -6.206e-01 6.966e-02 -8.908 < 2e-16
is_urbanTRUE -2.667e-01 7.474e-02 -3.569 0.000358
water_source_cleanProtected Shallow Well 4.947e-01 8.496e-02 5.823 5.79e-09
water_source_cleanProtected Spring 1.279e+00 4.384e-01 2.917 0.003530
Intercept ***
distance_to_tertiary_road ***
distance_to_city ***
distance_to_town ***
water_point_population ***
local_population_1km ***
usage_capacity1000 ***
is_urbanTRUE ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6534.5 on 4755 degrees of freedom
Residual deviance: 5688.9 on 4746 degrees of freedom
AIC: 5708.9
Number of Fisher Scoring iterations: 5
AICc: 5708.923
Pseudo R-square value: 0.129406
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 2377.371
Regression points: the same locations as observations are used.
Distance metric: A distance matrix is specified for this model calibration.
************Summary of Generalized GWR coefficient estimates:**********
Min. 1st Qu. Median
Intercept -3.7021e+02 -4.3797e+00 3.5590e+00
distance_to_tertiary_road -3.1622e-02 -4.5462e-04 9.1291e-05
distance_to_city -5.4555e-02 -6.5623e-04 -1.3507e-04
distance_to_town -8.6549e-03 -5.2754e-04 -1.6785e-04
water_point_population -2.9696e-02 -2.2705e-03 -1.2277e-03
local_population_1km -7.7730e-02 4.4281e-04 1.0548e-03
usage_capacity1000 -5.5889e+01 -1.0347e+00 -4.1960e-01
is_urbanTRUE -7.3554e+02 -3.4675e+00 -1.6596e+00
water_source_cleanProtected.Shallow.Well -1.8842e+02 -4.7295e-01 6.2378e-01
water_source_cleanProtected.Spring -1.3630e+03 -5.3436e+00 2.7714e+00
3rd Qu. Max.
Intercept 1.3755e+01 2171.6375
distance_to_tertiary_road 6.3011e-04 0.0237
distance_to_city 1.5921e-04 0.0162
distance_to_town 2.4490e-04 0.0179
water_point_population 4.5879e-04 0.0765
local_population_1km 1.8479e-03 0.0333
usage_capacity1000 3.9113e-01 9.2449
is_urbanTRUE 1.0554e+00 995.1841
water_source_cleanProtected.Shallow.Well 1.9564e+00 66.8914
water_source_cleanProtected.Spring 7.0805e+00 208.3749
************************Diagnostic information*************************
Number of data points: 4756
GW Deviance: 2815.659
AIC : 4418.776
AICc : 4744.213
Pseudo R-square value: 0.5691072
***********************************************************************
Program stops at: 2022-12-18 00:36:38 7.4.2 Convert Data Frame
gwr.fixed_calibr <- as.data.frame(gwlr.fixed_calibr$SDF)7.4.3 Set Threshold Value
gwr.fixed_calibr <- gwr.fixed_calibr %>%
mutate(most = ifelse(
gwr.fixed_calibr$yhat >= 0.5, T, F))7.4.4 Generate Confusion Matrix
gwr.fixed_calibr$y <- as.factor(gwr.fixed_calibr$y)
gwr.fixed_calibr$most <- as.factor(gwr.fixed_calibr$most)
CM <- confusionMatrix(data = gwr.fixed_calibr$most,
reference = gwr.fixed_calibr$y)
CMConfusion Matrix and Statistics
Reference
Prediction FALSE TRUE
FALSE 1833 268
TRUE 281 2374
Accuracy : 0.8846
95% CI : (0.8751, 0.8935)
No Information Rate : 0.5555
P-Value [Acc > NIR] : <2e-16
Kappa : 0.7661
Mcnemar's Test P-Value : 0.6085
Sensitivity : 0.8671
Specificity : 0.8986
Pos Pred Value : 0.8724
Neg Pred Value : 0.8942
Prevalence : 0.4445
Detection Rate : 0.3854
Detection Prevalence : 0.4418
Balanced Accuracy : 0.8828
'Positive' Class : FALSE
7.5 Visualise GWLR
wp_osun.sf_selected_calibr <- wp_osun.sf %>%
select(c(ADM2_EN, ADM2_PCODE, ADM1_EN, ADM1_PCODE, status))gwr_sf.fixed_calibr <- cbind(wp_osun.sf_selected_calibr, gwr.fixed_calibr)7.6 Visualise Functional & Non-Functional Water Point
tmap_mode("view")tmap mode set to interactive viewingprob_TCalibr <- tm_shape(bdy_osun) +
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed_calibr) +
tm_dots(col = "yhat",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(9,14))
prob_TCalibrtmap_mode("plot")tmap mode set to plotting8 REFERENCE
Chua A. (2022). In-class Ex5: Modelling the Spatial Variation of the Explanatory Factors of Water Point Status using Geographically Weighted Logistic Regression. https://isss624-amelia.netlify.app/exercises/in-class_ex5/in-class_ex5